The times of all 15 year olds who run a certain race are approximately normally distributed with a given mean = 18 sec and standard deviation = 1.2 sec. What percentage of the runners have times less than 14.4 sec?
A)0.15%
B)0.30%
C)0.60%
D)2.50%

Question

The times of all 15 year olds who run a certain race are approximately normally distributed with a given mean = 18 sec and standard deviation = 1.2 sec. What percentage of the runners have times less than 14.4 sec?
A)0.15%
B)0.30%
C)0.60%
D)2.50%

kirbykirby · Answer

If $X$ is the time of a 15-yr old runner, then you are interested in $P(X < 14.4)$.

You can standardize $X$ with the formula: $Z=\dfrac{X-\mu}{\sigma} $ where $\mu$  is the mean, $\sigma$ is the std. deviation.

kirbykirby · Answer

$$P(X<14.4)=P\left(\frac{X-18}{1.2} <\frac{14.4-18}{1.2}\right)=P(Z<-3) $$